Multimodal Dependent Type Theory

We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by mode specifies collection of modes, modalities, and transformations between them. show that different choices allow us to use the same compute reason in many modal situations, including guarded recursion, axiomatic cohesion, parametric quantification. reproduce examples from prior work recursion thereby demonstrating constitutes simple usable syntax whose instantiations intuitively correspond previous handcrafted theories. In some cases, instantiating particular situation unearths previously unknown improves upon systems. Finally, we investigate metatheory MTT. prove consistency establish canonicity through an extension recent type-theoretic gluing techniques. These results hold irrespective choice theory, thus apply wide variety situations.